CN115234257A - Secondary lining large-volume concrete construction method suitable for ultra-large span tunnel circular curve segment - Google Patents

Secondary lining large-volume concrete construction method suitable for ultra-large span tunnel circular curve segment Download PDF

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Publication number
CN115234257A
CN115234257A CN202211063185.1A CN202211063185A CN115234257A CN 115234257 A CN115234257 A CN 115234257A CN 202211063185 A CN202211063185 A CN 202211063185A CN 115234257 A CN115234257 A CN 115234257A
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China
Prior art keywords
support
section
pouring
concrete
secondary lining
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CN202211063185.1A
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Chinese (zh)
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CN115234257B (en
Inventor
李言
张长军
姜辉
谭忠盛
杨明
王志辉
王建宇
曾宇乐
付新
何毅
张俊宏
徐铎
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Beijing Jiaotong University
China Railway 16th Bureau Group Co Ltd
Road and Bridge Engineering Co Ltd of China Railway 16th Bureau Group Co Ltd
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Beijing Jiaotong University
China Railway 16th Bureau Group Co Ltd
Road and Bridge Engineering Co Ltd of China Railway 16th Bureau Group Co Ltd
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Priority to CN202211063185.1A priority Critical patent/CN115234257B/en
Publication of CN115234257A publication Critical patent/CN115234257A/en
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Publication of CN115234257B publication Critical patent/CN115234257B/en
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    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21DSHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
    • E21D11/00Lining tunnels, galleries or other underground cavities, e.g. large underground chambers; Linings therefor; Making such linings in situ, e.g. by assembling
    • E21D11/04Lining with building materials
    • E21D11/10Lining with building materials with concrete cast in situ; Shuttering also lost shutterings, e.g. made of blocks, of metal plates or other equipment adapted therefor
    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21DSHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
    • E21D11/00Lining tunnels, galleries or other underground cavities, e.g. large underground chambers; Linings therefor; Making such linings in situ, e.g. by assembling
    • E21D11/04Lining with building materials
    • E21D11/10Lining with building materials with concrete cast in situ; Shuttering also lost shutterings, e.g. made of blocks, of metal plates or other equipment adapted therefor
    • E21D11/105Transport or application of concrete specially adapted for the lining of tunnels or galleries ; Backfilling the space between main building element and the surrounding rock, e.g. with concrete
    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21DSHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
    • E21D11/00Lining tunnels, galleries or other underground cavities, e.g. large underground chambers; Linings therefor; Making such linings in situ, e.g. by assembling
    • E21D11/04Lining with building materials
    • E21D11/10Lining with building materials with concrete cast in situ; Shuttering also lost shutterings, e.g. made of blocks, of metal plates or other equipment adapted therefor
    • E21D11/107Reinforcing elements therefor; Holders for the reinforcing elements

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  • Engineering & Computer Science (AREA)
  • Structural Engineering (AREA)
  • Architecture (AREA)
  • Mining & Mineral Resources (AREA)
  • Civil Engineering (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Geochemistry & Mineralogy (AREA)
  • Geology (AREA)
  • Lining And Supports For Tunnels (AREA)

Abstract

The invention provides a construction method suitable for secondary lining of a circular curve segment of a super-large span tunnel with large-volume concrete, which comprises the following steps: s1, dividing a circular curve segment into a plurality of construction segments with approximately equal lengths; s2, performing a pre-pressing test on part of the construction sections to determine parameters of the support and the template; s3, removing the temporary supporting structure of the pouring construction section, and detecting and protecting the constructed section and the pouring construction section: s4, erecting a template, erecting a support according to a rectangle, and detecting support foundation settlement and support body, wherein the long edge of the support is adjacent to the secondary lining of the constructed section; s5, simultaneously pouring concrete on two sides of the support, calculating the difference of the concrete pouring amount of the two sides after the concrete reaches the arch forming line, and balancing the weight of the empty template outside the inner contour line of the secondary lining by using a sand bag; s6, curing the construction section in which the concrete is poured; the method provided by the invention can eliminate the horizontal component force difference at two sides of the support, prevent the support from generating horizontal displacement and avoid the deviation and platform dislocation of the secondary lining.

Description

Secondary lining large-volume concrete construction method suitable for ultra-large span tunnel circular curve segment
Technical Field
The invention relates to the technical field of civil engineering construction, in particular to a construction method suitable for secondary lining large-volume concrete of a circular curve section of a super-large span tunnel.
Background
For the secondary lining of a straight-line tunnel, a trolley method or a rack method is generally adopted for construction, but for the secondary lining construction of a circular curve section tunnel, because the circular curve section tunnel is not only in a circular arc shape in the transverse section but also in a circular arc shape in the longitudinal direction, the irregular shape is difficult to meet the pouring requirement if the conventional trolley method or the rack method is adopted for secondary lining; in addition, the sizes of the inner side and the outer side of the circular curve section tunnel are inconsistent, and the pouring amount of the concrete on the outer side is larger than that on the inner side during secondary lining, so that the horizontal acting component force of the concrete poured on the outer side on a template and a supporting structure is larger than that on the inner side, particularly in the circular curve section part of the oversized cross-over tunnel with the thickness of the secondary lining exceeding 1 meter, the horizontal acting component force difference of the inner side and the outer side is larger, the supporting structure is easy to generate horizontal displacement, and the problems of secondary lining deviation, slab staggering and the like are caused.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide the construction method which can prevent the horizontal displacement of the supporting structure and avoid the deviation and dislocation of the secondary lining and is suitable for the secondary lining of the circular curve section of the ultra-large cross-tunnel and large-volume concrete.
The present invention achieves the above object by:
the invention relates to a construction method suitable for secondary lining of a circular curve section of an oversized cross-tunnel and large-volume concrete, which comprises the following steps:
the method comprises the following steps of S1, dividing a circular curve section of a tunnel into a plurality of construction sections with approximately equal lengths according to the length of the circular curve section;
s2, selecting a test section from the plurality of construction sections, and performing a pre-pressing test on the test section to determine the deformation of the support and the template and the reasonable pre-camber of the support;
s3, dismantling the temporary support structure of the pouring construction section in the tunnel, and well detecting and protecting the constructed section and the pouring construction section;
s4, erecting a support and a template, and arranging reinforcing steel bars, wherein the support is erected according to a rectangular structure, the long edge of the support is adjacent to a secondary lining of a constructed section, and the foundation settlement of the support and the monitoring of a support body of the support are well carried out;
s5, pouring secondary lining concrete on two sides of the support, keeping the height of concrete surfaces on two sides of the support approximately the same in the pouring process, starting to record the concrete pouring amount on two sides of the support and calculate the difference after the concrete pouring of the straight wall section is finished and enters an arch raising line, and balancing the balance of the concrete pouring amount on two sides of the support by using a sand bag on a vacant template outside a poured secondary lining inner contour line;
and S6, curing the construction section in which the concrete is poured, and removing the template and the support after the curing period is over.
Further, in the step S4, the setting up the support further includes shortening a distance between two adjacent ring arches in the support, so that the ring arches 5 are arranged more closely; a plurality of longitudinal edges are additionally arranged in the support at equal intervals along the cross section of the tunnel, and the annular arch center of the support is supported by the longitudinal edges; an inclined support and an inner support are additionally arranged in the bracket; a pull rod is additionally arranged at the end head of the outer side of the support and is connected with a longitudinal beam of the support; and additionally arranging a compression bar on the outer side of the support, wherein one end of the compression bar is used for performing back pressure on the primary support of the non-construction section beside the inner contour of the pouring construction section through a backing plate and a wedge block.
Further, in the step S2, the pre-pressing test includes applying pressure to the test section, and calculating a pre-pressing load by using a widest position outside the standard construction section as a standard.
Further, in the step S3, the total length of the temporary supporting structure to be dismantled should be greater than the length of the pouring construction section (meeting the requirement of a scaffold erection working surface).
Further, in the step S5, the pouring of the secondary lining concrete includes pouring according to a symmetry principle, pouring concrete from the arch springing at two sides of the support, pouring from the arch springing to the arch raising line in the longitudinal direction at the straight wall section, and after reaching the arch raising line, pouring symmetrically in a segmented and layered manner along the arch span direction, so that the pouring speed at two ends is accurately controlled, and the layered thickness is not more than 500mm.
The invention has the beneficial effects that:
the invention provides a construction method for secondarily lining large-volume concrete suitable for a circular curve section of a super-large span tunnel, which is used for secondarily lining the circular curve section of the tunnel by adopting a support method, and overcomes the defect that the existing rack method or trolley method is not matched with the circular curve section of the tunnel and is difficult to meet the casting requirement of the circular curve section.
Drawings
The invention is further illustrated with reference to the following figures and examples:
FIG. 1 is a schematic top view of a tunnel circular curve segment divided into construction segments;
FIG. 2 is a schematic cross-sectional view of a tunnel circular curve segment after a support is built at a part of a pouring construction segment;
FIG. 3 is an enlarged view of A in FIG. 2;
FIG. 4 is a schematic top view of a support of a partially poured construction section of a circular curve section of a tunnel;
FIG. 5 is an enlarged view of B in FIG. 4;
fig. 6 is a schematic diagram of a sandbag counterweight in a construction section poured by a circular curve section of a tunnel.
In the figure, 1-the outer contour of a circular curve section of a tunnel, 2-the inner contour of the circular curve section of the tunnel, 3-a division line of a construction section, 4-a design central axis of the tunnel, 5-an annular arch frame, 6-a wedge block, 7-an adjustable upright post, 8-a longitudinal edge, 9-an inclined strut, 10-a secondary lining of the constructed section, 11-the constructed section, 12-a bracket, 13-a non-construction section, 14-a compression bar, 15-a base plate, 16-a good concrete secondary lining and 17-a sand bag counterweight.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the following examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not to be construed as limiting the present invention.
Fig. 1 to 6 show a construction method for secondary lining of a large-volume concrete suitable for a circular curve segment of a super-large span tunnel in an embodiment of the invention, which specifically comprises the following steps:
s1, dividing a circular curve section of a tunnel into a plurality of construction sections with approximately equal lengths according to the length of the circular curve section.
As shown in fig. 1, according to the length of an outer contour 1 and the length of an inner contour 2 of a circular curve segment part of a tunnel, the circular curve segment part is divided into a plurality of construction segments with approximately equal length along the direction of a design central axis 4 of the tunnel, and the range of each construction segment is defined by a construction boundary 3.
And S2, selecting a test section from the plurality of construction sections, and performing a pre-pressing test on the test section to determine the deformation of the support and the template and the reasonable pre-camber of the support.
Selecting at least one appropriate construction section from the divided construction sections as a test section, carrying out a pre-pressing test on the test section, determining design parameters of a support and a template for secondary lining according to the result of the pre-pressing test, including the deformation of the support and the template and the reasonable pre-camber of the support, wherein the pre-pressing test comprises the steps of carrying out the pre-pressing test on the test section based on a support method, arranging a support model in the test section by designing the support model, applying pressure on the test section, calculating the pre-pressing load of the support by taking the widest part at the outer side of the standard construction section as the reference, and determining and adjusting the design parameters of the support and the template for the secondary lining according to the pre-pressing load.
And S3, dismantling the temporary support structure of the pouring construction section in the tunnel, and detecting and protecting the constructed section and the pouring construction section.
Before the next construction section is subjected to concrete pouring, detection and protection measures are firstly taken for the construction section 11 in which concrete is poured and the pouring construction section prepared for pouring, so that safety accidents are prevented from occurring in the construction process, then a temporary supporting structure in the pouring construction section is dismantled, and a support and a template for secondary lining are prepared, wherein the total length of the temporary supporting structure to be dismantled is larger than that of the pouring construction section, so that the requirement of a working surface built by the support is met.
And S4, erecting a support and a template, and arranging reinforcing steel bars, wherein the support is erected according to a rectangular structure, the long edge of the support is adjacent to the secondary lining 10 of the constructed section 11, and the foundation settlement of the support and the monitoring of a support frame body are well performed.
As shown in fig. 2, 3, 4 and 5, a support 12 for secondary lining is erected in a rectangular structure, the long side of the entire support 12 is adjacent to the secondary lining of the constructed section 11, and the support 12 is erected by using a plurality of beams, longitudinal beams, and ring arches 5, and is installed in the support 12
In order to weaken and eliminate horizontal unbalance caused by the inconsistency between the concrete pouring amount of the inner contour 2 and the outer contour 1 of the circular curve section of the tunnel, to make the bracket 12 for secondary lining more stable and less deformable, and to make the structure of the bracket 12 better cover the pouring construction section, as shown in fig. 2 and 3, in addition to erecting the bracket 12 in a rectangular structure so that the long side of the bracket 12 abuts against the construction section where the secondary lining is completed, the improvement of the bracket 12 comprises:
the distance between two adjacent annular arches 5 in the support 12 is shortened, so that the annular arches 5 are arranged more closely; a plurality of longitudinal ribs 8 are additionally arranged in the bracket 12 at equal intervals along the cross section of the tunnel, and the annular arch frame 5 of the bracket 12 is supported by the longitudinal ribs 8; an inner support and an inclined support 9 are additionally arranged in the bracket 12; a pull rod is additionally arranged at the end head of the outer side of the support 12 and is connected with a longitudinal beam of the support 12; and a compression bar 14 is additionally arranged on the outer side of the bracket 12, and one end of the compression bar 14 is used for back pressure of the primary support of the non-construction section 13 beside the inner contour of the pouring construction section through a backing plate 15 and a wedge-shaped block 6.
Wherein, the distance between two adjacent ring-shaped arches 5 in the bracket 12 is shortened, so that the two adjacent ring-shaped arches 5 are closer, which is beneficial to enhancing the deformation resistance of the connecting part connected with the two adjacent ring-shaped arches 5, so that the bracket 12 is stable, and the ring-shaped arches 5 are made of I-shaped steel;
the arrangement of the longitudinal edge 8 is specifically that a plurality of adjustable vertical rods 7 are arranged in the support 12 at equal intervals along the cross section direction of the tunnel, the longitudinal edge 8 is arranged at the tops of the adjustable vertical rods 7, wedge blocks 6 are arranged at the tops of the longitudinal edge 8, the heights of the longitudinal edge 8 and the wedge blocks 6 can be adjusted through the adjustable vertical rods 7, so that the longitudinal edge 8 can support the annular arch frame 5 of the support 12 through the wedge blocks 6, and the longitudinal edge 8 is made of i-steel;
the inclined strut 9 is connected with the longitudinal beam part of the bracket 12, the top end of the inclined strut 9 is connected with the annular arch frame 5, and the bottom end of the inclined strut 9 is connected with the tunnel ground (which is the specific inner support, which is not shown in the figure)
A pull rod is arranged at the outer end of the bracket 12, one end of the pull rod is abutted against the tunnel ground, the other end of the pull rod pulls the longitudinal beam part of the bracket 12, and the horizontal acting component force borne by the bracket 12 is reduced or offset by utilizing the pulling force of the pull rod on the bracket 12;
generally, the bending degree of the outer contour at the tunnel circular curve section is greater than that of the inner contour, when the square-shaped bracket 12 is provided, the fitting degree of the bracket 12 and the outer contour is greater than that of the bracket 12 and the inner contour, so that there is inevitably a problem that the stress distribution of the bracket 12 adjacent to both sides of the outer and inner contours is unbalanced, the gap between the bracket 12 and the outer contour is smaller than that between the bracket 12 and the inner contour, and meanwhile, the casting amount of the concrete at the outer contour is generally greater than that of the concrete at the inner contour, the horizontal acting component force of the concrete at the outer contour to the bracket 12 is greater than that of the concrete at the inner contour, when there is a problem of the stress difference between both sides of the bracket 12 and the stress distribution imbalance, the bracket 12 is easily displaced and deformed, and in order to weaken or eliminate the negative influence of the stress difference and the stress distribution imbalance, it is necessary to additionally provide the outer side of the bracket 12 adjacent to one side of the construction section, and one side of the compression bar 14 is connected to the bracket 12, the problem that the bracket 12 is not displaced and the support bar 12 is pressed by the inner contour 6, and the wedge-shaped support bar 12 is reduced, and the problem that the initial stress distribution of the bracket 12 is not unbalanced.
And S5, pouring secondary lining concrete on two sides of the support 12, keeping the height of concrete surfaces on two sides of the support 12 approximately the same in the pouring process, recording the concrete pouring amount on two sides of the support 12 and calculating the difference after the concrete pouring of the straight wall section is finished and an arch line is entered, and balancing the balance of the concrete pouring amount on two sides of the support 12 by using a sand bag 17 on a vacant template outside the inner contour line of the poured secondary lining 16 to balance the difference of the concrete pouring amount on two sides of the support 12.
Pouring concrete, starting from arch feet on two sides of the support 12, along the contour of the support 12, firstly, pouring a straight wall section and then an arch part, and pouring according to a symmetrical principle, wherein the height of concrete surfaces on two sides of the support 12 is kept approximately the same in the pouring process, when the pouring of the concrete at the straight wall section is finished, the arch part is poured from an arch lifting line, the pouring is symmetrically performed in a subsection mode along the arch span direction, the pouring speed of the two ends is accurately controlled, the thickness of the pouring in the subsection mode is not more than 500mm, when the arch part is poured, the height of the concrete surfaces on two sides of the support 12 is continuously kept approximately the same, meanwhile, the pouring amount of the concrete on two sides of the support 12 is recorded, so that the difference is calculated, sand bags 17 with the same weight as the difference are prepared according to the difference, and after the pouring is finished, as shown in figure 6, the sand bags 17 are immediately weighted on the empty templates outside the inner contour line of the poured secondary lining 16, and the difference of the pouring amount of the concrete pouring on two sides of the support 12 is balanced by the sand bags 17, so that the difference of the horizontal acting force on the difference of the horizontal acting force on the two sides of the support 12 is reduced or eliminated.
And S6, curing the construction section in which the concrete is poured, and removing the template and the support 12 after the curing period is over.
The curing of the constructed section 11 is essentially performed, and after the concrete is solidified and the curing period expires, the support 12 and the formwork are removed.
It is to be understood that the foregoing examples, while indicating the preferred embodiments of the invention, are given by way of illustration and description, and are not to be construed as limiting the scope of the invention; it should be noted that, for a person skilled in the art, the above technical features can be freely combined, and several changes and modifications can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention; therefore, all equivalent changes and modifications made within the spirit and scope of the present invention should be covered by the appended claims.

Claims (5)

1. A construction method suitable for secondary lining of a circular curve section of an oversized cross-tunnel and large-volume concrete is characterized by comprising the following steps: the method comprises the following steps of S1, dividing a circular curve section of a tunnel into a plurality of construction sections with approximately equal lengths according to the length of the circular curve section; s2, selecting a test section from the plurality of construction sections, and carrying out a pre-pressing test on the test section to determine the deformation of the support (12) and the template and the reasonable pre-camber of the support; s3, dismantling the temporary support structure of the pouring construction section in the tunnel, and well detecting and protecting the constructed section (11) and the pouring construction section; s4, erecting a support (12) and a template, and arranging steel bars, wherein the support (12) is erected according to a rectangular structure, the long edge of the support (12) is adjacent to a secondary lining (10) of a constructed section (11), and the settlement of a support foundation and the monitoring of a support body are well performed; s5, pouring secondary lining concrete on two sides of the support (12), keeping the height of concrete surfaces on two sides of the support approximately the same in the pouring process, starting to record the concrete pouring amount on two sides of the support (12) and calculate the difference when concrete pouring of a straight wall section is finished and enters an arch line, and balancing the balance of the concrete pouring amount on two sides of the support (12) by using a sand bag on a vacant template outside an inner contour line of the poured secondary lining (16); and S6, curing the construction section in which the concrete is poured, and removing the template and the support after the curing period is over.
2. The construction method of the secondary lining large-volume concrete suitable for the circular curve segment of the ultra-large cross tunnel according to claim 1, characterized in that: in the step S4, the erecting the support (12) further includes shortening a distance between two adjacent circular arches (5) in the support (12), so that the circular arches (5) are arranged more closely; a plurality of longitudinal ribs (8) are additionally arranged in the support (12) at equal intervals along the cross section of the tunnel, and the annular arch frame (5) of the support (12) is supported by the longitudinal ribs (8); an inclined support (9) and an inner support are additionally arranged in the bracket (12); a pull rod is additionally arranged at the end head of the outer side of the support (12), and the pull rod is connected with a longitudinal beam of the support (12); and a compression bar (14) is additionally arranged on the outer side of the support (12), and one end of the compression bar (14) is used for back-pressure primary support of a non-construction section (13) beside the inner contour of the pouring construction section through a backing plate (15) and a wedge block (6).
3. The construction method of the secondary lining large-volume concrete suitable for the circular curve segment of the ultra-large cross tunnel according to claim 1, characterized in that: in the step S2, the pre-pressing test includes applying pressure to the test section, and calculating a pre-pressing load with a widest position outside the standard construction section as a standard.
4. The construction method of the secondary lining large-volume concrete suitable for the circular curve segment of the ultra-large cross tunnel according to claim 1, characterized in that: in the step S3, the total length of the temporary supporting structure to be dismantled should be greater than the length of the pouring construction section.
5. The construction method of the secondary lining mass concrete suitable for the circular curve segment of the ultra-large span tunnel according to claim 1, characterized in that: in the step S5, the secondary lining concrete pouring comprises the steps of pouring according to a symmetry principle, pouring concrete from the arch springing positions on two sides of the support (12), pouring from the arch springing positions to the arch camber line in the longitudinal direction at the straight wall section, and after reaching the arch camber line, performing subsection layering symmetrical pouring along the arch span direction, wherein the pouring speed at two ends is accurately controlled, and the layering thickness is not more than 500mm.
CN202211063185.1A 2022-08-31 2022-08-31 Construction method suitable for secondary lining of circular curve section of oversized-span tunnel and large-volume concrete Active CN115234257B (en)

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Citations (5)

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Publication number Priority date Publication date Assignee Title
JPH08184299A (en) * 1994-12-28 1996-07-16 Fujita Corp Placing method for lining concrete of tunnel and device thereof
JP2012062667A (en) * 2010-09-15 2012-03-29 Fudo Tetra Corp Curing method of lining concrete and curing material used in the method
CN108915725A (en) * 2018-06-12 2018-11-30 中铁二十局集团轨道交通工程有限公司 A kind of small template lining construction method in double -side approach tunnel
CN109083658A (en) * 2018-06-27 2018-12-25 昆明理工大学 Using concrete filled steel tube as the Tunnel Second Lining structure and its construction method of skeleton
CN216198282U (en) * 2021-10-21 2022-04-05 中国化学工程第十六建设有限公司 Underground passage inverted arch drainage structure

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH08184299A (en) * 1994-12-28 1996-07-16 Fujita Corp Placing method for lining concrete of tunnel and device thereof
JP2012062667A (en) * 2010-09-15 2012-03-29 Fudo Tetra Corp Curing method of lining concrete and curing material used in the method
CN108915725A (en) * 2018-06-12 2018-11-30 中铁二十局集团轨道交通工程有限公司 A kind of small template lining construction method in double -side approach tunnel
CN109083658A (en) * 2018-06-27 2018-12-25 昆明理工大学 Using concrete filled steel tube as the Tunnel Second Lining structure and its construction method of skeleton
CN216198282U (en) * 2021-10-21 2022-04-05 中国化学工程第十六建设有限公司 Underground passage inverted arch drainage structure

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
刘志春;李文江;孙明磊;朱永全;: "乌鞘岭隧道F4断层区段监控量测综合分析", 岩石力学与工程学报, no. 07, 28 July 2006 (2006-07-28) *
莫立胜;: "双线隧道仰拱整体式浇筑台车的研制及应用", 铁道建筑技术, no. 12, 20 December 2015 (2015-12-20) *

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